rus
Issue #1/2019
A. M. Grigoriev, E. V. Cherkesova
See The Invisible: Visualization Of Physical Fields In Semiconductor Materials
See The Invisible: Visualization Of Physical Fields In Semiconductor Materials
This article deals with the results of theoretical and experimental studies of the possibilities of visualizing the effects of external thermal, electromagnetic and acoustic fields on a semiconductor material by radiation from the spectral range of the material’s fundamental absorption edge.
DOI: 10.22184/1993-7296.FRos.2019.13.1.50.57
DOI: 10.22184/1993-7296.FRos.2019.13.1.50.57
Теги: semiconductor materials visualizing of acoustic fields visualizing of electromagnetic fields visualizing of thermal fields визуализация акустических полей визуализация тепловых полей визуализация электромагнитных полей полупроводниковые материалы
INTRODUCTION
There are many ways to visualize various physical fields. The temperature field of a heated body can be viewed contact-free with thermal imagers and IR cameras. The contact methods for observing thermal fields are based on the use of various heat-sensitive media, e. g., liquid crystals. Magnetic fields are visualized by means of ferromagnetic powders and liquids. Mechanical stress fields in transparent media are observed using polarized light in crossed polarizers. The electric field lines can be seen by applying a suspension of an electropolarizing powder in a viscous liquid dielectric, such as ebonite powder in castor oil.
All of the above and other methods of visual observation of physical fields are based on various principles of the interaction of fields with visualization media or the surrounding space. However, in the case of materials with a energy gap, such as semiconductors, crystalline dielectrics, and some glasses, it is possible to visually observe various fields inside the material, based on one physical effect. This is the effect of a change of the bandgap and, accordingly, a shift of the material’s fundamental absorption edge, which is induced by a particular physical field. As a result of external influence of a thermal, mechanical, electric or magnetic field on a semiconductor material, its energy gap may increase or decrease. So, when heated, the gap increases, and under the conditions of compression of the material, e. g., influenced by hydrostatic pressure, the width of the gap decreases.
PHYSICAL PRINCIPLE OF VISUALIZATION
It is known that materials with an energy gap are transparent to light if the energy of the incident photon is less than the width of the energy gap, and completely absorbs light if the energy of the incident photon turns out to be greater than this width. The spectral region of the transition from transparency to absorption is referred to as the fundamental absorption edge of the material. The coefficient of light absorption by the material increases exponentially, and this process is described by the Urbach formula [1]:
,
where: Eg is the energy gap of a semiconductor, E is the photon energy; EU is the Urbach parameter; α0 is the material absorption coefficient at E = Eg.
If the energy gap Eg changes by a certain amount ±ΔEg, then this leads to a shift of the intrinsic absorption edge to the short-wave or long-wave region of the spectrum, respectively, the sign of the change in the bandgap. This edge shift effect can be used to visually observe the result of various external influences on the material: mechanical, acoustic, thermal, as well as electric and magnetic fields. To form an optical image of the result of an external impact, the material needs to be illuminated with a probe beam of light with photon energy from the spectral region, where the photon energy is slightly less than the width of the energy gap and which is referred to as the tail of the absorption edge.
For light with a fixed photon energy, Eph from the spectral region of the absorption tail, the change in the absorption coefficient under conditions of a change in the gap size is determined by the relation that follows from the Urbach formula [2]:
where: is the initial material absorption coefficient of light with photon energy Eph (until the moment of the beginning of the impact).
In the case of an external impact on the material, leading to a decrease in the gap by the value –ΔEg, the absorption edge shifts to the left, to the long wavelength side of the spectrum. This shift causes a significant increase in the absorption coefficient of light with the photon energy Eph and, accordingly, the attenuation of light passing through the material. If the material is under the influence of increasing the energy gap +ΔEg, then the absorption edge shifts to the right in the direction of short waves. During the edge shift process, the absorption coefficient of light with a photon energy Eph is significantly reduced, the material becomes clear in proportion to the degree of external influence, and the amount of light passing through the material increases. This situation is shown schematically in Figure 1. The green curve is the absorption edge before external influence, and the red and blue curves represent the long-wavelength and short-wavelength shift of the edge, respectively, the photon energy Eph is denoted with a yellow dotted line.
Since different external influences on a material with an energy gap cause a multidirectional shift of its own absorption edge, it is advisable to consider the issue of visualization, dividing external influences into two types. The first type induces an increase in the energy gap material and the edge shift to the long-wave side of the spectrum, and the second type causes a decrease in the gap and a shift of the edge to the short-wave side.
LONG-WAVELENGTH SHIFT
Heating a semiconductor material or an electric field causes a decrease in the energy gap, which is proportional to the change in material temperature or field strength, respectively.
In the case of heating a semiconductor material initially under normal conditions (temperature 20 °C and atmospheric pressure ~105 Pa), the reduction of the gap is directly proportional to the increase in temperature:
,
where: ζ is the coefficient of temperature change of the gap, ΔT is the change in the temperature of the material as a result of heating.
For a static electric field, the gap change can be estimated using the relation given in [3]:
,
where: e is the electron charge, Eel is the electric field strength, mef is the effective electron mass.
It was shown in [4] that the relation connecting the change in the gap with the field strength is also valid in the case of an alternating electric field, including the field of the light wave, provided that the photon energy is much less than the width of the gap. In this case, the change in the gap is associated with the intensity of the light wave by the following relation [3]:
,
where I is the intensity of the light wave; n is the refractive index of the material.
SHORT-WAVELENGTH SHIFT
An increase in the energy gap and a shift of the absorption edge of a semiconductor material to the long-wavelength side of the spectrum is observed when a material with semiconductor properties is affected by hydrostatic pressure, mechanical compressive stresses and a magnetic field; in the case of mechanical compressive stresses, the change in the energy gap is directly proportional to the pressure:
ΔEg(P) = νP,
where: ν is the coefficient associating the change in the gap with the amount of pressure applied to the material, P is the pressure.
The change in the semiconductor bandgap, which is in a magnetic field (where B is the value of magnetic induction), is described by the formula:
.
In both cases, the external influence on the semiconductor of pressure, compressive stress or magnetic field increases the energy gap, and the absorption edge shifts to the short-wavelength side of the spectrum.
EXAMPLES OF VISUALIZATION OF EXTERNAL INFLUENCES ON SEMICONDUCTOR MATERIAL
The method of visualizing the result of external influences in both cases of the edge shift is based on the transmission of the material by the probing light beam with a uniform intensity distribution in the beam cross section and the wavelength from the spectral region of the absorption tail. In the case of local or non-uniform in space of any of the external effects listed above, a light beam passing through the material will acquire an amplitude relief corresponding to the spatial distribution of the degree of impact on the material. In this case, lens or mirror optics can be used to form a light image of the result of an external impact on the material. It is obvious that images obtained as a result of opposite edge shifts will be related to each other as positive and negative.
The verification of the proposed physical principle of visualization of various external influences on the semiconductor material was performed on samples of gallium arsenide, which were subjected to thermal and acoustic effects. These types of effects are chosen because they cause a multidirectional shift of the self-absorption edge of the semiconductor material. The edge shift in the field of a powerful light wave was studied in detail in [4].
The local thermal effect on the semiconductor wafer was made due to the absorption of a CO2 laser radiation pulse. The plate was made of n-type gallium arsenide with a concentration of free carriers of 1018 cm–3. A laser pulse with a duration of 80 µs was focused on the surface of the plate into a spot with a diameter of about 1.5 mm and was absorbed by free carriers, which provided local heating of the sample area with a transverse size corresponding to the diameter of the laser spot. At the moment of the end of the heating laser pulse, the plate was transilluminated by a beam of radiation from a semiconductor pulsed laser LPI‑14 with a wavelength of 905 nm, which corresponds to the edge of the intrinsic absorption of gallium arsenide at room temperature. The pulse duration of a semiconductor laser had a value of ~100 ns. As a result of local heating, the absorption edge of gallium arsenide shifted to the long-wavelength side of the spectrum and the transmission beam, which initially had a uniform intensity distribution after passing through the plate, acquired a negative amplitude relief corresponding to the heat distribution in the sample. Further, with a lens with a focal length of 50 mm was used to form an image of local heating of the plate on the matrix of a CCD camera (Fig. 2).
It should be noted that the heating image repeats the distribution of the intensity of the CO2-laser radiation – the TEM01 mode.
As an example of visualization of the impact, increasing the area of the semiconductor material, an acoustic wave was chosen, which was induced by exposing the sample to a focused pulse of a neodymium laser with a duration of 12 nanoseconds. The pulse was partially absorbed by the sample material, which caused the generation of an acoustic wave. With a delay of several microseconds, the plate was transilluminated by a probe radiation pulse with parameters identical to the case of visualization of thermal exposure. In the region of the maxima of the acoustic wave, the plate material was compressed, which led to the shift of the absorption edge to the short-wave side of the spectrum and a decrease in absorption at the wavelength of the transmission radiation, which after passing through the plate acquired a positive amplitude relief. As in the previous case, the image of the impact was formed by a lens and recorded with a CCD camera. Fig. 3 shows an image of an acoustic wave induced in a gallium arsenide plate by a pulse of a neodymium laser.
As expected, the images of thermal and acoustic effects are correlated as negative and positive, which is explained by the multidirectional shift of the edge of the intrinsic absorption of the sample material.
CONCLUSION
Shifting the edges of the intrinsic absorption of a material that has an energy gap allows visualization of various external effects on the material, which makes it possible to solve a very wide range of technical problems.
Thus, with reference to laser technology, based on the visualization of a thermal field induced by laser radiation passing through a plate of a semiconductor material, such as GaAs, ZnSe or ZnS, you can create pass-through meters of high-intensity laser energy. It is also possible to realize optical sensors of various physical quantities. Also, applying fiber-optic delivery of translucent radiation to a small-sized semiconductor sensitive element, you can make fiber-optic solid-state pressure, temperature, and electric and magnetic fields.
Visualization of external influences can be applied to measure the physical parameters of semiconductor materials. By successively recording the images of heat or acoustic wave propagating in the material, it is possible to determine the thermal and acoustic parameters of the material: thermal conductivity coefficient or wave velocity, respectively. Furthermore, the imaging method can be useful for studying the stress state of semiconductor materials, e. g., electronic chips in the course of their work.
Thus, the proposed method of visualization of various external influences on materials with semiconductor properties can be very useful in practice.
There are many ways to visualize various physical fields. The temperature field of a heated body can be viewed contact-free with thermal imagers and IR cameras. The contact methods for observing thermal fields are based on the use of various heat-sensitive media, e. g., liquid crystals. Magnetic fields are visualized by means of ferromagnetic powders and liquids. Mechanical stress fields in transparent media are observed using polarized light in crossed polarizers. The electric field lines can be seen by applying a suspension of an electropolarizing powder in a viscous liquid dielectric, such as ebonite powder in castor oil.
All of the above and other methods of visual observation of physical fields are based on various principles of the interaction of fields with visualization media or the surrounding space. However, in the case of materials with a energy gap, such as semiconductors, crystalline dielectrics, and some glasses, it is possible to visually observe various fields inside the material, based on one physical effect. This is the effect of a change of the bandgap and, accordingly, a shift of the material’s fundamental absorption edge, which is induced by a particular physical field. As a result of external influence of a thermal, mechanical, electric or magnetic field on a semiconductor material, its energy gap may increase or decrease. So, when heated, the gap increases, and under the conditions of compression of the material, e. g., influenced by hydrostatic pressure, the width of the gap decreases.
PHYSICAL PRINCIPLE OF VISUALIZATION
It is known that materials with an energy gap are transparent to light if the energy of the incident photon is less than the width of the energy gap, and completely absorbs light if the energy of the incident photon turns out to be greater than this width. The spectral region of the transition from transparency to absorption is referred to as the fundamental absorption edge of the material. The coefficient of light absorption by the material increases exponentially, and this process is described by the Urbach formula [1]:
,
where: Eg is the energy gap of a semiconductor, E is the photon energy; EU is the Urbach parameter; α0 is the material absorption coefficient at E = Eg.
If the energy gap Eg changes by a certain amount ±ΔEg, then this leads to a shift of the intrinsic absorption edge to the short-wave or long-wave region of the spectrum, respectively, the sign of the change in the bandgap. This edge shift effect can be used to visually observe the result of various external influences on the material: mechanical, acoustic, thermal, as well as electric and magnetic fields. To form an optical image of the result of an external impact, the material needs to be illuminated with a probe beam of light with photon energy from the spectral region, where the photon energy is slightly less than the width of the energy gap and which is referred to as the tail of the absorption edge.
For light with a fixed photon energy, Eph from the spectral region of the absorption tail, the change in the absorption coefficient under conditions of a change in the gap size is determined by the relation that follows from the Urbach formula [2]:
where: is the initial material absorption coefficient of light with photon energy Eph (until the moment of the beginning of the impact).
In the case of an external impact on the material, leading to a decrease in the gap by the value –ΔEg, the absorption edge shifts to the left, to the long wavelength side of the spectrum. This shift causes a significant increase in the absorption coefficient of light with the photon energy Eph and, accordingly, the attenuation of light passing through the material. If the material is under the influence of increasing the energy gap +ΔEg, then the absorption edge shifts to the right in the direction of short waves. During the edge shift process, the absorption coefficient of light with a photon energy Eph is significantly reduced, the material becomes clear in proportion to the degree of external influence, and the amount of light passing through the material increases. This situation is shown schematically in Figure 1. The green curve is the absorption edge before external influence, and the red and blue curves represent the long-wavelength and short-wavelength shift of the edge, respectively, the photon energy Eph is denoted with a yellow dotted line.
Since different external influences on a material with an energy gap cause a multidirectional shift of its own absorption edge, it is advisable to consider the issue of visualization, dividing external influences into two types. The first type induces an increase in the energy gap material and the edge shift to the long-wave side of the spectrum, and the second type causes a decrease in the gap and a shift of the edge to the short-wave side.
LONG-WAVELENGTH SHIFT
Heating a semiconductor material or an electric field causes a decrease in the energy gap, which is proportional to the change in material temperature or field strength, respectively.
In the case of heating a semiconductor material initially under normal conditions (temperature 20 °C and atmospheric pressure ~105 Pa), the reduction of the gap is directly proportional to the increase in temperature:
,
where: ζ is the coefficient of temperature change of the gap, ΔT is the change in the temperature of the material as a result of heating.
For a static electric field, the gap change can be estimated using the relation given in [3]:
,
where: e is the electron charge, Eel is the electric field strength, mef is the effective electron mass.
It was shown in [4] that the relation connecting the change in the gap with the field strength is also valid in the case of an alternating electric field, including the field of the light wave, provided that the photon energy is much less than the width of the gap. In this case, the change in the gap is associated with the intensity of the light wave by the following relation [3]:
,
where I is the intensity of the light wave; n is the refractive index of the material.
SHORT-WAVELENGTH SHIFT
An increase in the energy gap and a shift of the absorption edge of a semiconductor material to the long-wavelength side of the spectrum is observed when a material with semiconductor properties is affected by hydrostatic pressure, mechanical compressive stresses and a magnetic field; in the case of mechanical compressive stresses, the change in the energy gap is directly proportional to the pressure:
ΔEg(P) = νP,
where: ν is the coefficient associating the change in the gap with the amount of pressure applied to the material, P is the pressure.
The change in the semiconductor bandgap, which is in a magnetic field (where B is the value of magnetic induction), is described by the formula:
.
In both cases, the external influence on the semiconductor of pressure, compressive stress or magnetic field increases the energy gap, and the absorption edge shifts to the short-wavelength side of the spectrum.
EXAMPLES OF VISUALIZATION OF EXTERNAL INFLUENCES ON SEMICONDUCTOR MATERIAL
The method of visualizing the result of external influences in both cases of the edge shift is based on the transmission of the material by the probing light beam with a uniform intensity distribution in the beam cross section and the wavelength from the spectral region of the absorption tail. In the case of local or non-uniform in space of any of the external effects listed above, a light beam passing through the material will acquire an amplitude relief corresponding to the spatial distribution of the degree of impact on the material. In this case, lens or mirror optics can be used to form a light image of the result of an external impact on the material. It is obvious that images obtained as a result of opposite edge shifts will be related to each other as positive and negative.
The verification of the proposed physical principle of visualization of various external influences on the semiconductor material was performed on samples of gallium arsenide, which were subjected to thermal and acoustic effects. These types of effects are chosen because they cause a multidirectional shift of the self-absorption edge of the semiconductor material. The edge shift in the field of a powerful light wave was studied in detail in [4].
The local thermal effect on the semiconductor wafer was made due to the absorption of a CO2 laser radiation pulse. The plate was made of n-type gallium arsenide with a concentration of free carriers of 1018 cm–3. A laser pulse with a duration of 80 µs was focused on the surface of the plate into a spot with a diameter of about 1.5 mm and was absorbed by free carriers, which provided local heating of the sample area with a transverse size corresponding to the diameter of the laser spot. At the moment of the end of the heating laser pulse, the plate was transilluminated by a beam of radiation from a semiconductor pulsed laser LPI‑14 with a wavelength of 905 nm, which corresponds to the edge of the intrinsic absorption of gallium arsenide at room temperature. The pulse duration of a semiconductor laser had a value of ~100 ns. As a result of local heating, the absorption edge of gallium arsenide shifted to the long-wavelength side of the spectrum and the transmission beam, which initially had a uniform intensity distribution after passing through the plate, acquired a negative amplitude relief corresponding to the heat distribution in the sample. Further, with a lens with a focal length of 50 mm was used to form an image of local heating of the plate on the matrix of a CCD camera (Fig. 2).
It should be noted that the heating image repeats the distribution of the intensity of the CO2-laser radiation – the TEM01 mode.
As an example of visualization of the impact, increasing the area of the semiconductor material, an acoustic wave was chosen, which was induced by exposing the sample to a focused pulse of a neodymium laser with a duration of 12 nanoseconds. The pulse was partially absorbed by the sample material, which caused the generation of an acoustic wave. With a delay of several microseconds, the plate was transilluminated by a probe radiation pulse with parameters identical to the case of visualization of thermal exposure. In the region of the maxima of the acoustic wave, the plate material was compressed, which led to the shift of the absorption edge to the short-wave side of the spectrum and a decrease in absorption at the wavelength of the transmission radiation, which after passing through the plate acquired a positive amplitude relief. As in the previous case, the image of the impact was formed by a lens and recorded with a CCD camera. Fig. 3 shows an image of an acoustic wave induced in a gallium arsenide plate by a pulse of a neodymium laser.
As expected, the images of thermal and acoustic effects are correlated as negative and positive, which is explained by the multidirectional shift of the edge of the intrinsic absorption of the sample material.
CONCLUSION
Shifting the edges of the intrinsic absorption of a material that has an energy gap allows visualization of various external effects on the material, which makes it possible to solve a very wide range of technical problems.
Thus, with reference to laser technology, based on the visualization of a thermal field induced by laser radiation passing through a plate of a semiconductor material, such as GaAs, ZnSe or ZnS, you can create pass-through meters of high-intensity laser energy. It is also possible to realize optical sensors of various physical quantities. Also, applying fiber-optic delivery of translucent radiation to a small-sized semiconductor sensitive element, you can make fiber-optic solid-state pressure, temperature, and electric and magnetic fields.
Visualization of external influences can be applied to measure the physical parameters of semiconductor materials. By successively recording the images of heat or acoustic wave propagating in the material, it is possible to determine the thermal and acoustic parameters of the material: thermal conductivity coefficient or wave velocity, respectively. Furthermore, the imaging method can be useful for studying the stress state of semiconductor materials, e. g., electronic chips in the course of their work.
Thus, the proposed method of visualization of various external influences on materials with semiconductor properties can be very useful in practice.
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